Biharmonic Riemannian Submersions from the Product Space M2×R
In this paper, we study biharmonic Riemannian submersions π : M 2 × R → ( N 2 , h ) from a product manifold onto a surface and obtain some local characterizations of such biharmonic maps. Our results show that when the target surface is flat, a proper biharmonic Riemannian submersion π : M 2 × R → (...
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| Veröffentlicht in: | The Journal of geometric analysis 2025, Vol.35 (1) |
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| container_title | The Journal of geometric analysis |
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| creator | Wang, Ze-Ping Ou, Ye-Lin |
| description | In this paper, we study biharmonic Riemannian submersions
π
:
M
2
×
R
→
(
N
2
,
h
)
from a product manifold onto a surface and obtain some local characterizations of such biharmonic maps. Our results show that when the target surface is flat, a proper biharmonic Riemannian submersion
π
:
M
2
×
R
→
(
N
2
,
h
)
is locally a projection of a special twisted product, and when the target surface is non-flat,
π
is locally a special map between two warped product spaces with a warping function that solves a single ODE. As a by-product, we also prove that there is a unique proper biharmonic Riemannian submersion
H
2
×
R
→
R
2
given by the projection of a warped product onto the Euclidean plane. |
| doi_str_mv | 10.1007/s12220-024-01828-x |
| format | Article |
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π
:
M
2
×
R
→
(
N
2
,
h
)
from a product manifold onto a surface and obtain some local characterizations of such biharmonic maps. Our results show that when the target surface is flat, a proper biharmonic Riemannian submersion
π
:
M
2
×
R
→
(
N
2
,
h
)
is locally a projection of a special twisted product, and when the target surface is non-flat,
π
is locally a special map between two warped product spaces with a warping function that solves a single ODE. As a by-product, we also prove that there is a unique proper biharmonic Riemannian submersion
H
2
×
R
→
R
2
given by the projection of a warped product onto the Euclidean plane.</description><identifier>ISSN: 1050-6926</identifier><identifier>EISSN: 1559-002X</identifier><identifier>DOI: 10.1007/s12220-024-01828-x</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Convex and Discrete Geometry ; Differential Geometry ; Dynamical Systems and Ergodic Theory ; Euclidean geometry ; Fourier Analysis ; Global Analysis and Analysis on Manifolds ; Mathematics ; Mathematics and Statistics</subject><ispartof>The Journal of geometric analysis, 2025, Vol.35 (1)</ispartof><rights>Mathematica Josephina, Inc. 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p72x-9ec0e05e0ead93b8f3ed223bfcad0f8ed5f124dd7fc6efc4562cf92618ee124e3</cites><orcidid>0009-0003-4548-3376</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12220-024-01828-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12220-024-01828-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Wang, Ze-Ping</creatorcontrib><creatorcontrib>Ou, Ye-Lin</creatorcontrib><title>Biharmonic Riemannian Submersions from the Product Space M2×R</title><title>The Journal of geometric analysis</title><addtitle>J Geom Anal</addtitle><description>In this paper, we study biharmonic Riemannian submersions
π
:
M
2
×
R
→
(
N
2
,
h
)
from a product manifold onto a surface and obtain some local characterizations of such biharmonic maps. Our results show that when the target surface is flat, a proper biharmonic Riemannian submersion
π
:
M
2
×
R
→
(
N
2
,
h
)
is locally a projection of a special twisted product, and when the target surface is non-flat,
π
is locally a special map between two warped product spaces with a warping function that solves a single ODE. As a by-product, we also prove that there is a unique proper biharmonic Riemannian submersion
H
2
×
R
→
R
2
given by the projection of a warped product onto the Euclidean plane.</description><subject>Abstract Harmonic Analysis</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Euclidean geometry</subject><subject>Fourier Analysis</subject><subject>Global Analysis and Analysis on Manifolds</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1050-6926</issn><issn>1559-002X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2025</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkM9KAzEQh4MoWKsv4CngOTqZbPbPRdBiVagobQ_eljQ7sVvc7Jp0oW_iA_lirlbwNAPzMb8fH2PnEi4lQHYVJSKCAEwEyBxzsTtgI6l1IQDw9XDYQYNIC0yP2UmMG4AkVUk2Yte39dqEpvW15fOaGuN9bTxf9KuGQqxbH7kLbcO3a-Ivoa16u-WLzljiT_j1OT9lR868Rzr7m2O2nN4tJw9i9nz_OLmZiS7DnSjIAoEmIFMVapU7RRWiWjlrKnA5VdpJTKoqczYlZxOdonVDV5kTDQdSY3axf9uF9qOnuC03bR_8kFgqiQVKLRUOlNpTsQu1f6PwT0kofzyVe0_l4Kn89VTu1DdK1ly3</recordid><startdate>2025</startdate><enddate>2025</enddate><creator>Wang, Ze-Ping</creator><creator>Ou, Ye-Lin</creator><general>Springer US</general><general>Springer Nature B.V</general><scope/><orcidid>https://orcid.org/0009-0003-4548-3376</orcidid></search><sort><creationdate>2025</creationdate><title>Biharmonic Riemannian Submersions from the Product Space M2×R</title><author>Wang, Ze-Ping ; Ou, Ye-Lin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p72x-9ec0e05e0ead93b8f3ed223bfcad0f8ed5f124dd7fc6efc4562cf92618ee124e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2025</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Euclidean geometry</topic><topic>Fourier Analysis</topic><topic>Global Analysis and Analysis on Manifolds</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Ze-Ping</creatorcontrib><creatorcontrib>Ou, Ye-Lin</creatorcontrib><jtitle>The Journal of geometric analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Ze-Ping</au><au>Ou, Ye-Lin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Biharmonic Riemannian Submersions from the Product Space M2×R</atitle><jtitle>The Journal of geometric analysis</jtitle><stitle>J Geom Anal</stitle><date>2025</date><risdate>2025</risdate><volume>35</volume><issue>1</issue><issn>1050-6926</issn><eissn>1559-002X</eissn><abstract>In this paper, we study biharmonic Riemannian submersions
π
:
M
2
×
R
→
(
N
2
,
h
)
from a product manifold onto a surface and obtain some local characterizations of such biharmonic maps. Our results show that when the target surface is flat, a proper biharmonic Riemannian submersion
π
:
M
2
×
R
→
(
N
2
,
h
)
is locally a projection of a special twisted product, and when the target surface is non-flat,
π
is locally a special map between two warped product spaces with a warping function that solves a single ODE. As a by-product, we also prove that there is a unique proper biharmonic Riemannian submersion
H
2
×
R
→
R
2
given by the projection of a warped product onto the Euclidean plane.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s12220-024-01828-x</doi><orcidid>https://orcid.org/0009-0003-4548-3376</orcidid></addata></record> |
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| ispartof | The Journal of geometric analysis, 2025, Vol.35 (1) |
| issn | 1050-6926 1559-002X |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Euclidean geometry Fourier Analysis Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics |
| title | Biharmonic Riemannian Submersions from the Product Space M2×R |
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